function t = trijacobi(n,a,b) %TRIJACOBI Returns the tridiagonal matrix of polynomial recurrence coefficients % TRIJACOBI(N,A,B) returns a tridiagonal matrix whose entries correspond % to the coefficients describing the recurrence between % the Jacobi Polynomials. % % The eigenvalues of this matrix correspond to the roots of the N-th % Jacobi polynomial with parameters A and B. % % N, A and B are integers. % % % References: % [1] Alan Edelman, Handout 6: Tridiagonal Matrices, Orthogonal % Polynomials ans the Classical Random Matrix % Ensembles, Fall 2004, % Course Notes 18.338. % [2] Alan Edelman, Random Matrix Eigenvalues. % [3] Gabor Szego, Orthogonal Polynomials, American Mathematical % Society, Providence, 1975. 4th Edition. % [4] Eric Weisstein, Jacobi Polynomial." From MathWorld-- % A Wolfram Web Resource. % http://mathworld.wolfram.com/JacobiPolynomial.htm % % Brian Sutton, Sept. 2004. % \$Revision: 1.0 \$ \$Date: 2004/09/23 11:35:18 \$ i = (1:n-1)'; d1 = 2*sqrt(i.*(a+i).*(b+i).*(a+b+i)./(-1+a+b+2*i)./(1+a+b+2*i))./(a+ ... b+2*i); d0 = -(a^2-b^2)./(a+b+2*(0:n-1)')./(2+a+b+2*(0:n-1)'); t = spdiags([[d1;0] d0 [0;d1]],[-1 0 1],n,n);